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A Way to Detect Bias

paulgraham.com

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Re: A Way to Detect Bias

#91

Post by pg »

WildUtah wrote: post #20

On a simple mathematical basis, this is false. Consider two groups of candidates for a scholarship, A and B. We want to select all candidates that have an 80% or better chance of graduation. Group A comes from a population where the chance of graduation is distributed uniformly from 0% to 100% and group B is from one where the chance is distributed uniformly from 10% to 90%, with the same average but less variation i…

It's true that this test assumes groups of applicants are roughly equal in (distribution of) ability. That is the default assumption in most conversations I've been involved in about bias, and particularly the example I used, but I'll add something making that explicit.

Re: A Way to Detect Bias

#92

Post by tansey »

yummyfajitas wrote: post #84
tansey wrote: post #79

Earlier quoted context omitted.

Sorry, I'm confused here. A p-value makes an implicit assumption that your null hypothesis is a known N(0,1). That may be throwing me off a bit. I get the point of you want to look at the likelihood function which is just one minus the CDF in the given interval. I'm just not clear on how you can get around f and g being arbitrarily parameterized functions of a given class. Are you assuming we know the class and somet…

A null hypothesis is just a specific thing you are trying to disprove. In this case, it's simply that the min of both distributions is identical. I am assuming we know exactly one thing about the class the measures f and g come from: for every function in that class, \int_C^{C+d} f(x) dx >= h(d) for some monotonic function h(d). The p-value is then computed in terms of h(d), since p >= h(d)^N.

Okay, I'll have to wait for your full write-up, because I am not seeing the path of thought here.

Re: A Way to Detect Bias

#93

Post by 55555 »

hibikir wrote: post #85
WildUtah wrote: post #20

On a simple mathematical basis, this is false. Consider two groups of candidates for a scholarship, A and B. We want to select all candidates that have an 80% or better chance of graduation. Group A comes from a population where the chance of graduation is distributed uniformly from 0% to 100% and group B is from one where the chance is distributed uniformly from 10% to 90%, with the same average but less variation i…

The problem here is language and what our actual objectives are. When people complain about bias, they are not really talking about mathematical bias, but about something else: Their idea of fairness. They are talking about discrimination. And when we are discussing that, we can't really think about whether rules are applied fairly or not, but whether the rules produce the outcomes that we want. Let's go for a ludicr…

Great comment. There are two types of fairness, (a) fair rules, and (b) fair outcome.

Re: A Way to Detect Bias

#94

Post by decisiveness »

eoi wrote: post #73
WildUtah wrote: post #20

On a simple mathematical basis, this is false. Consider two groups of candidates for a scholarship, A and B. We want to select all candidates that have an 80% or better chance of graduation. Group A comes from a population where the chance of graduation is distributed uniformly from 0% to 100% and group B is from one where the chance is distributed uniformly from 10% to 90%, with the same average but less variation i…

The article defines bias as follows: > Want to know if the selection process was biased against some type of applicant? Check whether they outperform the others. This is not just a heuristic for detecting bias. It's what bias means. Under that definition, you have been biased against A. [edit: on reflection I see this as a weakness of his definition. I missed that your selection process does in fact select the best c…

Unless you know what exactly caused A to outperform others, you won't really know if the process is biased or what made it biased.

When asserting biases, you must first distinguish them from random noise. Using pg's logic, every selection process that isn't perfect is biased.

Re: A Way to Detect Bias

#95

Post by yummyfajitas »

quietplatypus wrote: post #81
yummyfajitas wrote: post #33

People, most of whom clearly are not that good at math, are being really harsh on Paul Graham. Graham is mostly right, but slightly incorrect. In particular, suppose group A has the distribution f(x) and B has the distribution g(x). If f(x) and g(x) are shaped significantly differently past the cutoff , then mean(H(x-C)f(x)) and mean(H(x-c)g(x)) might not agree even though there is no bias by construction. (Here H(x)…

Isn't this not as meaningful as the mean, because the minimum doesnt really tell you about true capability? I can also easily construct an institution that satisfies your parameters, the minimums of two groups match, as in they have a token member at C for every group, but the characteristic performance of all members is different? This in my eyes amounts to a simplification that is neat mathematically, but removes m…

If you think you can construct examples that break my test, go ahead and do it. I'm curious to see what you can come up with.

However, your claim that you can have "a token member at C for every group" is merely the claim that adversarial sampling can destroy any statistical procedure. So what? This is boring mathematically. Nor is it relevant to the problem at hand unless you want to claim that First Round Capital is actively conspiring to both a) be biased and earn less money and b) waste more money hiding that bias by funding tokens.

Re: A Way to Detect Bias

#96

Post by yummyfajitas »

tprice7 wrote: post #78
yummyfajitas wrote: post #41

Earlier quoted context omitted.

Suppose the cutoff for men is C but for women is C+K. Then the weakest man can be expected to have quality C+epsilon, while the weakest woman will have quality C+K+epsilon. Here epsilon is how close a typical candidate will be to the cutoff, and is mainly a function of the sample size. I don't know the behavior of epsilon off the top of my head.

I think MattHeard understood this and his point was that the weakest man will realistically have quality C + epsilon + random, and the weakest woman will have quality C + K + epsilon + random. The random term arises because no evaluation process is going to perfectly tell you how people are going to end up performing. But yeah, this seems fixable also, by averaging some number of the lowest performing members of each…

I'm not 100% sure how to deal with noise + extremal statistics. But I've got a 12 hour plane ride ahead of me tomorrow, so I can probably work out a fix.

Re: A Way to Detect Bias

#97

Post by MichaelGG »

esfandia wrote: post #90
MichaelGG wrote: post #67

I don't understand his point about First Round Capital showing their female founders did better than companies without female founders. What does that show? How do we know that female founders aren't simply better? Or maybe women are scared of applying, so out of women, only the best apply? In that case, the mere idea that there is a bias can cause "pre-selection" bias. I lack the mathematics to prove this, but it se…

The argument is that First Round Capital must have implictly made it harder for female founders to get funding, since the ones who do perform better. The rational course of action for First Round Capital would be to lower their threshold on female founders (or, conversely, raise the threshold on male founders) until they perform no better or no worse than male founders.

And that's not proven by the evidence. It might be a good thing to look into, but pg's statement that you don't need more info is wrong.

Re: A Way to Detect Bias

#98

Post by tracker1 »

I just asume there is bias... I mean the fact is, bias is what youare trying to work in favor of... that bias being factors of success. Chasing your tail against random statistics won't really show much, and a person is more complex that a few statistical groups. As far as investing goes, there's also the product, and how that leader/founder matches to that product category itself. A founder that succeeds in one category won't definitively succeed in another. Many founders fail their first few times, and later succeed. Others fail after some success(es).

I think as long as reasonable steps are made to avoid certain obvious bias, the rest is mostly chance.

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